Using MATLAB to calculate the thermal efficiency and visualizing the PV diagram.

%inputs
gamma = 1.4
t3 = 2300
%state variables
p1 = 101325
t1 = 500
% engine geometric parameters
bore = 0.1;
stroke = 0.1;
con_rod = 0.15;
cr = 12;

%calculating the swapt volume and the clearance volume
v_swept = (pi/4)*bore^2*stroke;
v_clearance = v_swept/(cr-1);
v1 = v_swept + v_clearance 
v2 = v_clearance
%state variables at state point 2
%p2v2^gamma = p1v1^gamma
%p2 = p1*(v1/v2)^gamma = p1*cr^gamma
p2 = p1*cr^gamma;
%p1v1/t1 = p2v2/t2 | t2 = p2*v2*t1/(p1*v1)
t2 = p2*v2*t1/(p1*v1);

constant_c = p1*v1^gamma;
V_compression = engine_kinematics(bore,stroke,con_rod,cr,180,0);
P_compression = constant_c./V_compression.^gamma;

%state variables at state point 3
v3 = v2
%p3v3/t3 = p2v2/t2 | p3 = p2*t3/t2
p3 = p2*t3/t2

constant_c = p3*v3^gamma;
V_expansion = engine_kinematics(bore,stroke,con_rod,cr,0,180);
P_expansion = constant_c./V_expansion.^gamma;

%state variables at state point 4
v4 = v1

%p3v3^gamma = p4v4^gamma | p4 = p3(v3/v4)^gamma
p4 = p3*(v3/v4)^gamma

thermal_efficiency = 1-(1/(cr).^(gamma-1))

figure (1)
hold on
plot (v1,p1,'color','r')
plot (V_compression,P_compression)
plot([v3 v3],[p2 p3])
plot (v2,p2,'*','color','r')
plot (v3,p3,'*','color','r')
plot (V_expansion,P_expansion)
plot([v1 v1],[p4 p1])
plot (v4,p4,'*','color','r')

figure(2)
plot([v1 v2 v3 v4 v1],[p1 p2 p3 p4 p1],'color','b')

function [V] = engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)

a = stroke/2
R = con_rod/a
v_s= pi/4*bore^2*stroke;
v_c = v_s/(cr-1);
theta = linspace(start_crank,end_crank,180)
term1 = 0.5*(cr-1);
term2 = R +1 - cosd(theta);
term3 = (R^2-sind(theta).^2).^0.5;
V = (1+ term1*(term2-term3)).*v_c;


end

thermal_efficiency = 1-(1/(cr).^(gamma-1))

thermal_efficiency =

    0.6299

using matlab to calculate the thermal efficiency and visualizing the PV diagram of an otto cycle.

isentropic compression

constant volume heat addition

isentropic expansion

constant volume heat rejection